Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
Solve for x
Solve for r
x=3−1+1+3r2x=−31+1+3r2
Evaluate
r2−3x2−2x=0
Rewrite in standard form
−3x2−2x+r2=0
Multiply both sides
3x2+2x−r2=0
Substitute a=3,b=2 and c=−r2 into the quadratic formula x=2a−b±b2−4ac
x=2×3−2±22−4×3(−r2)
Simplify the expression
x=6−2±22−4×3(−r2)
Simplify the expression
More Steps
Evaluate
22−4×3(−r2)
Multiply
More Steps
Multiply the terms
4×3(−r2)
Rewrite the expression
−4×3r2
Multiply the terms
−12r2
22−(−12r2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
22+12r2
Evaluate the power
4+12r2
x=6−2±4+12r2
Simplify the radical expression
More Steps
Evaluate
4+12r2
Factor the expression
4(1+3r2)
The root of a product is equal to the product of the roots of each factor
4×1+3r2
Evaluate the root
More Steps
Evaluate
4
Write the number in exponential form with the base of 2
22
Reduce the index of the radical and exponent with 2
2
21+3r2
x=6−2±21+3r2
Separate the equation into 2 possible cases
x=6−2+21+3r2x=6−2−21+3r2
Simplify the expression
More Steps
Evaluate
x=6−2+21+3r2
Divide the terms
More Steps
Evaluate
6−2+21+3r2
Rewrite the expression
62(−1+1+3r2)
Cancel out the common factor 2
3−1+1+3r2
x=3−1+1+3r2
x=3−1+1+3r2x=6−2−21+3r2
Solution
More Steps
Evaluate
x=6−2−21+3r2
Divide the terms
More Steps
Evaluate
6−2−21+3r2
Rewrite the expression
62(−1−1+3r2)
Cancel out the common factor 2
3−1−1+3r2
Use b−a=−ba=−ba to rewrite the fraction
−31+1+3r2
x=−31+1+3r2
x=3−1+1+3r2x=−31+1+3r2
Show Solution
